Final answer:
4.00 moles of the gas that occupies 50.0 liters at a certain temperature and pressure will occupy 40.0 liters under the same conditions, as determined by Avogadro's Law.
Step-by-step explanation:
When dealing with gases and how they occupy space under certain conditions of temperature and pressure, we can use the Ideal Gas Law, or we can apply the direct relationship between the amount of gas and its volume at constant temperature and pressure known as Boyle's and Charles's Laws combined (Avogadro's Law). Here's how to solve the given problem:
According to Avogadro's Law, at the same temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. This means that if 5.00 moles of a gas occupy 50.0 liters, then 4.00 moles of the gas will occupy less volume in the same ratio. We use a simple proportion to solve the problem:
V1 / n1 = V2 / n2
Given that V1 is 50.0 L and n1 is 5.00 mol, and we're trying to find V2 when n2 is 4.00 mol:
50.0 L / 5.00 mol = V2 / 4.00 mol
Now, solve for V2:
V2 = (50.0 L * 4.00 mol) / 5.00 mol
V2 = 40.0 L
Therefore, 4.00 moles of the gas will occupy 40.0 liters under the same conditions of temperature and pressure.